Mathematical analysis of the transmission dynamics for malaria in individuals with varying levels of risk

Malaria continues to be a critical global health issue due to its profound impact on human development. This study explores the dynamics of malaria transmission within a population exhibiting multiple human susceptibilities, which arise from behavioral, locational, and occupational factors. We have formulated a nonlinear, time-dependent differential equation model to capture these dynamics. The model distinguishes between low- and high-risk susceptible human populations, offering a detailed analysis of malaria transmission patterns. We calculated the basic reproduction number R0, along with the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. The DFE is locally asymptotically stable when R0<1, while the EE is globally asymptotically stable when R0>1. Additionally, the model exhibits a backward bifurcation. Moreover, we have graphically illustrated the impact of multiple human susceptibilities. These effects become more evident over time: as the proportion of highly susceptible individuals within the population increases, the overall transmission rate rises accordingly. Furthermore, the mosquito-human contact rate and the mosquito death rate have exhibited effects consistent with our expectations.